Statistics for the Math Major

C.1: Develop mathematical thinking and communication skillsCourses designed for mathematical sciences majors should ensure
that students

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Gain experience in careful analysis of data;

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This month, I have chosen to address the second bullet of CUPM’s elaboration
of what it means to develop mathematical thinking and communication skills.
It is a point that will reappear in recommendation C.3 where the assertion is
made that students need to be aware of mathematics as stochastic as well as
mathematics as deterministic. In this recommendation, the phrase “analysis
of data” was chosen intentionally over “statistics” to make
it very clear that a course in probability would not be an acceptable substitute.

There are two strands to what it means to “gain experience in careful
analysis of data.” The first is that majors in the mathematical sciences
should be particularly adept at quantitative reasoning (QR). It may appear that
this comes automatically with a mathematics major, but that is not necessarily
the case. Over five years of refining our program in QR, Macalester College
has identified six skill sets that mark what we mean by basic QR. Students should
be able to

describe the world quantitatively,

evaluate sources and quality of data,

distinguish association from causation,

understand trade-offs,

understand uncertainty and risk,

use estimation and modeling to evaluate claims and test theories.

At many institutions, a major in mathematics by itself provides no guarantee
that a student can do any of these. A good course in statistics should address
these goals. A description of what constitutes a good course in introductory
statistics is available in the American Statistical Association’s GAISE
Report [1].

The second strand is more directly related to what our majors need as future
mathematicians. Information technology is shaping the direction of mathematics
for the 21st century, the development of Google’s search engine being
one of many illustrations of this. Understanding stochastic processes and how
to deal with large amounts of data are an essential part of mathematics, whether
this is for the student going directly to work as an “analyst” for
a large corporation, for the student who will hone mathematical skills in order
to bring them to bear on financial, health-related, or environmental problems,
or for the student pursuing a doctorate who might one day tackle the complex
mathematical problems now being generated by Biology, Chemistry, Economics,
and Physics.

For mathematicians to sideline statistics would be as serious a mistake as
that made by philosophers when they decided to exclude psychology, a field that
was growing within their own discipline. Philosophy would not have been subsumed
by its child. Rather, it could have been reinvigorated. Philosophy is poorer
today for the chasm that often lies between these disciplines.

Statistical thinking is part of mathematical thinking. Its importance is real
and growing. It needs to be addressed intentionally and specifically.

We would appreciate more examples that document experiences with the use of
technology as well as examples of interdisciplinary cooperation.

David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester
College in St. Paul, Minnesota, he was one of the writers for the Curriculum
Guide, and he currently serves as Chair of the CUPM. He wrote this column
with help from his colleagues in CUPM, but it does not reflect an official
position of the committee. You can reach him at bressoud@macalester.edu.